A Family of Symplectic Integrators: Stability, Accuracy, and Molecular Dynamics Applications

@article{Skeel1997AFO,
  title={A Family of Symplectic Integrators: Stability, Accuracy, and Molecular Dynamics Applications},
  author={Robert D. Skeel and Guihua Zhang and Tamar Schlick},
  journal={SIAM J. Scientific Computing},
  year={1997},
  volume={18},
  pages={203-222}
}
The following integration methods for special second-order ordinary differential equations are studied: leapfrog, implicit midpoint, trapezoid, Störmer–Verlet, and Cowell–Numerov. We show that all are members, or equivalent to members, of a one-parameter family of schemes. Some methods have more than one common form, and we discuss a systematic enumeration of these forms. We also present a stability and accuracy analysis based on the idea of “modified equations” and a proof of symplecticness… CONTINUE READING
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